A379532 Ulam numbers that are products of exactly four distinct primes (or tetraprimes).

390, 546, 690, 798, 1155, 1230, 1770, 2010, 2090, 2418, 2618, 2814, 3090, 3290, 3390, 3930, 4326, 4370, 4470, 4578, 4602, 4641, 6110, 6870, 7170, 7490, 7735, 7930, 8294, 9834, 10110, 10545, 10738, 11102, 11346, 11390, 11454, 11622, 11715, 11886, 12270, 12441, 12470, 12570

Offset

1,1

Comments

Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.

Links

Robert Israel, Table of n, a(n) for n = 1..6826

Example

390 is a term because 390=2*3*5*13 is the product of 4 distinct primes and 390 is an Ulam number.
546 is a term because 546=2*3*7*13 is the product of 4 distinct primes and 546 is an Ulam number.
1155 is a term because 1155=3*5*7*11 is the product of 4 distinct primes and 1155 is an Ulam number.

Maple

N:= 20000: # for terms <= N
U:= [1, 2]: V:= Vector(N): V[3]:= 1: R:= NULL: count:= 0:
for i from 3 do
   for k from U[-1]+1 to N do
     if V[k] = 1 then
       J:= select(`<=`, U +~ k, N);
       V[J]:= V[J] +~ 1;
       U:= [op(U), k];
       F:= ifactors(k)[2]:
       if F[.., 2] = [1, 1, 1, 1] then R:= R, k; count:= count+1;  fi;
       break
     fi
   od;
   if k > N then break fi;
od:
R; # Robert Israel, Dec 25 2024

Mathematica

seq[numUlams_] := Module[{ulams = {1, 2}}, Do[AppendTo[ulams, n = Last[ulams]; While[n++; Length[DeleteCases[Intersection[ulams, n - ulams], n/2, 1, 1]] != 2]; n], {numUlams}]; Select[ulams, FactorInteger[#][[;; , 2]] == {1, 1, 1, 1} &]]; seq[1200] (* Amiram Eldar, Dec 24 2024, after Jean-François Alcover at A002858 *)

Crossrefs

Intersection of A002858 and A046386.

Cf. A068820, A378795, A379162.

Sequence in context: A228580 A242182 A136153 * A069477 A325993 A108573

Adjacent sequences: A379529 A379530 A379531 * A379533 A379534 A379535

Keyword

nonn

Author

Massimo Kofler, Dec 24 2024

Status

approved